Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities

Section: New Results

Bayesian Nonparametrics

Participants : François Caron, Arnaud Doucet, Christopher Holmes, Jim Griffin, Dave Stephens.

Bayesian Nonparametric Models on Decomposable Graphs

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. These models are attractive because they ensure exchangeability (over samples). We propose here extensions of these models where the dependency between samples is given by a known decomposable graph. These models have appealing properties and can be easily learned using Markov Chain Monte Carlo and Sequential Monte Carlo techniques.

This work has been presented as an invited talk at the 7th workshop on Bayesian nonparametrics , Turin, Italy, and has been accepted at the NIPS international conference [8] .

Bayesian Nonparametric Models for two sample hypothesis testing

In this work [23] we describe Bayesian nonparametric procedures for two-sample hypothesis testing. That is, given two sets of samples Im1 ${\#119858 ^{(1)}\munder \#8764 \mtext iidF^{(1)}}$ and Im2 ${\#119858 ^{(2)}\munder \#8764 \mtext iidF^{(2)}}$ , with F(1), F(2) unknown, we wish to evaluate the evidence for the null hypothesis Im3 ${H_0:F^{(1)}\#8801 F^{(2)}}$ verses the alternative H1:F(1)$ \ne$F(2) . Our method is based upon a nonparametric Polya tree prior centered either a priori or empirically. We show that the Polya tree prior allows us to calculate an analytic expression for the marginal likelihood under the two hypotheses and hence provide an explicit measure of Im4 ${P(H_0|{{\#119858 ^{(1)},\#119858 ^{(2)}}})}$ .


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